The Genus Fields of Algebraic Number Fields PDF Download
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Author: M. Ishida
Publisher: Springer
ISBN: 3540375538
Category : Mathematics
Languages : en
Pages : 123
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Book Description
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Author: M. Ishida
Publisher: Springer
ISBN: 3540375538
Category : Mathematics
Languages : en
Pages : 123
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Book Description
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Author: Makoto Ishida
Publisher: Springer
ISBN: 9780387080000
Category : Algebraic fields
Languages : en
Pages : 115
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Book Description
Author: Makoto Ishida
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Albrecht Fröhlich
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 724
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Book Description
Author:
Publisher: Academic Press
ISBN: 0080873707
Category : Mathematics
Languages : en
Pages : 233
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Book Description
Algebraic Number Fields
Author: P.M. Cohn
Publisher: CRC Press
ISBN: 1351086480
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
Author: David Hilbert
Publisher: Springer Science & Business Media
ISBN: 9783540627791
Category : Mathematics
Languages : en
Pages : 402
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Book Description
A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Author: Emil Artin
Publisher: American Mathematical Soc.
ISBN: 0821840754
Category : Mathematics
Languages : en
Pages : 366
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Book Description
Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
Author: P E Conner
Publisher: World Scientific
ISBN: 9814513520
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Every finite separable field extension F/K carries a canonical inner product, given by trace(xy). This symmetric K-bilinear form is the trace form of F/K.When F is an algebraic number field and K is the field Q of rational numbers, the trace form goes back at least 100 years to Hermite and Sylvester. These notes present the first systematic treatment of the trace form as an object in its own right. Chapter I discusses the trace form of F/Q up to Witt equivalence in the Witt ring W(Q). Special attention is paid to the Witt classes arising from normal extensions F/Q. Chapter II contains a detailed analysis of trace forms over p-adic fields. These local results are applied in Chapter III to prove that a Witt class X in W(Q) is represented by the trace form of an extension F/Q if and only if X has non-negative signature. Chapter IV discusses integral trace forms, obtained by restricting the trace form of F/Q to the ring of algebraic integers in F. When F/Q is normal, the Galois group acts as a group of isometries of the integral trace form. It is proved that when F/Q is normal of prime degree, the integral form is determined up to equivariant integral equivalence by the discriminant of F alone. Chapter V discusses the equivariant Witt theory of trace forms of normal extensions F/Q and Chapter VI relates the trace form of F/Q to questions of ramification in F. These notes were written in an effort to identify central problems. There are many open problems listed in the text. An introduction to Witt theory is included and illustrative examples are discussed throughout.
Author: Gabriel Daniel Villa Salvador
Publisher: Springer Science & Business Media
ISBN: 0817645152
Category : Mathematics
Languages : en
Pages : 658
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Book Description
The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.
